102,863
edits
Changes
From Nordan Symposia
Jump to navigationJump to searchCreated page with "File:lighterstill.jpgright|frame ==Origin== late [http://nordan.daynal.org/wiki/index.php?title=English#ca._1100-1500_.09T..."
[[File:lighterstill.jpg]][[File:Multiplication as scaling integers.gif|right|frame]]
==Origin==
late [http://nordan.daynal.org/wiki/index.php?title=English#ca._1100-1500_.09THE_MIDDLE_ENGLISH_PERIOD Middle English]: from Old French, or from [[Latin]] multiplicatio(n-), from ''multiplicare''
*[http://en.wikipedia.org/wiki/14th_century]
==Definitions==
*1: the [[act]] or [[process]] of multiplying : the state of being multiplied
*2.a : a [[mathematical]] operation that at its simplest is an abbreviated process of adding an [https://en.wikipedia.org/wiki/Integer integer] to itself a specified [[number]] of times and that is extended to other numbers in accordance with [[laws]] that are valid for integers
:b : any of various mathematical operations that are analogous in some way to multiplication of the [https://en.wikipedia.org/wiki/Real_number real numbers] but are defined for other or larger sets of elements (as [https://en.wikipedia.org/wiki/Complex_number complex numbers], [[vectors]], [[matrices]], or functions)
==Description==
'''Multiplication''' (often denoted by the cross [[symbol]] "×", by a point "·" or by the [[absence]] of symbol) is one of the four elementary, mathematical operations of arithmetic; with the others being [https://en.wikipedia.org/wiki/Addition addition[, [https://en.wikipedia.org/wiki/Subtraction subtraction] and [https://en.wikipedia.org/wiki/Division_%28mathematics%29 division].
The multiplication of two [https://en.wikipedia.org/wiki/Natural_number whole numbers] is equivalent to adding as many copies of one of them, as the [[value]] of the other one:
[[File:Multiplication1.jpg|center]]
For example, 3 multiplied by 4 (often said as "3 times 4") can be calculated by adding 3 copies of 4 together:
[[File:Multiplication2.jpg|center]]
Here 3 and 4 are the "factors" and 12 is the "product".
One of the main properties of multiplication is the commutative property, adding 3 copies of 4 gives the same result as adding 4 copies of 3:
[[File:Multiplcation3.jpg|center]]
The multiplication of ]https://en.wikipedia.org/wiki/Integer integers] (including negative numbers), [https://en.wikipedia.org/wiki/Rational_number rational numbers] (fractions) and [https://en.wikipedia.org/wiki/Real_number real numbers] is defined by a systematic generalization of this basic [[definition]].
''Multiplication'' can also be [[visualized]] as counting objects arranged in a [https://en.wikipedia.org/wiki/Rectangle rectangle] (for whole numbers) or as finding the area of a rectangle whose sides have given lengths. The area of a rectangle does not depend on which side is measured first, which illustrates the commutative property.
The inverse operation of the multiplication is the division. For example, since 4 multiplied by 3 equals 12, then 12 divided by 3 equals 4. Multiplication by 3, followed by division by 3, yields the original number (since the division of a number other than 0 by itself equals 1).
Multiplication is also defined for other types of numbers, such as [https://en.wikipedia.org/wiki/Complex_number complex numbers], and more [[abstract]] constructs, like [[matrices]]. For these more abstract constructs, the order that the operands are multiplied sometimes does matter.[https://en.wikipedia.org/wiki/Multiplication]
[[Category: Mathematics]]
==Origin==
late [http://nordan.daynal.org/wiki/index.php?title=English#ca._1100-1500_.09THE_MIDDLE_ENGLISH_PERIOD Middle English]: from Old French, or from [[Latin]] multiplicatio(n-), from ''multiplicare''
*[http://en.wikipedia.org/wiki/14th_century]
==Definitions==
*1: the [[act]] or [[process]] of multiplying : the state of being multiplied
*2.a : a [[mathematical]] operation that at its simplest is an abbreviated process of adding an [https://en.wikipedia.org/wiki/Integer integer] to itself a specified [[number]] of times and that is extended to other numbers in accordance with [[laws]] that are valid for integers
:b : any of various mathematical operations that are analogous in some way to multiplication of the [https://en.wikipedia.org/wiki/Real_number real numbers] but are defined for other or larger sets of elements (as [https://en.wikipedia.org/wiki/Complex_number complex numbers], [[vectors]], [[matrices]], or functions)
==Description==
'''Multiplication''' (often denoted by the cross [[symbol]] "×", by a point "·" or by the [[absence]] of symbol) is one of the four elementary, mathematical operations of arithmetic; with the others being [https://en.wikipedia.org/wiki/Addition addition[, [https://en.wikipedia.org/wiki/Subtraction subtraction] and [https://en.wikipedia.org/wiki/Division_%28mathematics%29 division].
The multiplication of two [https://en.wikipedia.org/wiki/Natural_number whole numbers] is equivalent to adding as many copies of one of them, as the [[value]] of the other one:
[[File:Multiplication1.jpg|center]]
For example, 3 multiplied by 4 (often said as "3 times 4") can be calculated by adding 3 copies of 4 together:
[[File:Multiplication2.jpg|center]]
Here 3 and 4 are the "factors" and 12 is the "product".
One of the main properties of multiplication is the commutative property, adding 3 copies of 4 gives the same result as adding 4 copies of 3:
[[File:Multiplcation3.jpg|center]]
The multiplication of ]https://en.wikipedia.org/wiki/Integer integers] (including negative numbers), [https://en.wikipedia.org/wiki/Rational_number rational numbers] (fractions) and [https://en.wikipedia.org/wiki/Real_number real numbers] is defined by a systematic generalization of this basic [[definition]].
''Multiplication'' can also be [[visualized]] as counting objects arranged in a [https://en.wikipedia.org/wiki/Rectangle rectangle] (for whole numbers) or as finding the area of a rectangle whose sides have given lengths. The area of a rectangle does not depend on which side is measured first, which illustrates the commutative property.
The inverse operation of the multiplication is the division. For example, since 4 multiplied by 3 equals 12, then 12 divided by 3 equals 4. Multiplication by 3, followed by division by 3, yields the original number (since the division of a number other than 0 by itself equals 1).
Multiplication is also defined for other types of numbers, such as [https://en.wikipedia.org/wiki/Complex_number complex numbers], and more [[abstract]] constructs, like [[matrices]]. For these more abstract constructs, the order that the operands are multiplied sometimes does matter.[https://en.wikipedia.org/wiki/Multiplication]
[[Category: Mathematics]]
